Weird solidify results
1: (Not necessary but to simplify things) remove the Mirror and Solidify modifier.

2: Open the Viewport Shading menu and enable Backface Culling.



Now the problem is revealed. Mesh faces only have one side, With backface culling enabled we can see this. Your models has half the faces facing outwards (which is good) and the other half facing inwards (which is not good). To correct this 

3: In Edit mode select all of the mesh and open the Mesh menu, Mesh > Normals > Recalculate Outside.



4: Look carefully where the face is selected in the screenshot below and you will see a face that should not be there. Delete this face and fill in the gap it leaves.


5: Now you can add back the modifiers


Looks ok now :) ................

........... apart from the weird edge flow ! 
As with most things but especially cars, edge flow is very important. I suggest you find a car modeling tutorial on Youtube and pay special attention to that.
Takes time, sometimes you will spend hours and hours just tweaking existing vertices until it is ............ just right.

Edited to illustrate Nicola's suggestion in the comments 


Edited to reply to comment:
Often its extrude in one direction and the face normals are ok, extrude in the opposite direction and  you find the face normals are now reversed.Work with backface culling enabled and you will notice problems and can fix them as you go along.

Advice on edge flow? Spend a few hours watching car modeling tutorials on You tube.
Avoid Ngons and tris where possible and most important of all keep it as low poly as possible. The more geometry you have the harder it is to tweak.

Try for something similar to the screenshot below. 

Note this is only the side of the car. If I was intending to model the complete car, at the same time as adding the circles for the wheel arches I would also have added a circle for the front radiator grill and work back from there.





For this Youtube is going to be your best friend. Good luck.